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assert from 'assert';\nimport { BigRational } from 'big-rational-ts';\nimport * as types from './types.js';\n\nconst ZERO = new BigRational(0n, 1n);\n\nfunction maxRational(a: BigRational, b: BigRational) {\n return a.gt(b) ? a : b;\n}\n\nfunction minRational(a: BigRational, b: BigRational) {\n return a.lt(b) ? a : b;\n}\n\n/**\n * Computes the next state of the portfolio after an interaction.\n * @param prices The prices of the assets in ADA\n * @param targetWeights The target weights of the assets in the portfolio\n * @param state The current state of the portfolio\n * @param adaInput The amount of ADA to be added (if negative removed) to the portfolio\n *\n * @returns The new state of the portfolio\n */\nexport function computeInteraction(\n prices: types.Prices,\n targetWeights: types.Weights,\n state: types.PortfolioState,\n adaInput: BigRational,\n): types.PortfolioState {\n /** How much per asset in ADA in the portfolio before the deposit */\n const adaPerToken: types.RationalDict = {};\n\n const tvl = Object.entries(state.assets).reduce(\n (accTvl, [asset, assetAmount]) => {\n adaPerToken[asset] = new BigRational(assetAmount, 1n).mul(prices[asset]);\n return accTvl.add(adaPerToken[asset]);\n },\n ZERO,\n );\n\n /**\n * First condition: At least for one token in the collection,\n * there is a state for which this asset has the same amount of tokens\n * and the portfolio is balanced without removing tokens of a\n * different asset (i.e., it only needs to add tokens to the rest)\n *\n * Notice that tokens that satisfy this condition,\n * maximize the worth of tokens needed to reach balance.\n * If we find the asset with the max worth, we can know the minimum\n * amount of ADA needed to balance the portfolio.\n */\n\n const [maybeBalancedTokens, adaLeft] = getTokensToBalance(\n prices,\n targetWeights,\n adaPerToken,\n tvl,\n adaInput,\n );\n\n /**\n * Only enters here when the assets are actually balanced and there is more to\n * change in the portfolio\n */\n const adaLeftToModify = adaInput.gte(ZERO)\n ? adaLeft.gt(ZERO)\n : adaLeft.lt(ZERO);\n\n if (adaLeftToModify) {\n for (const [asset, amount] of Object.entries(maybeBalancedTokens)) {\n maybeBalancedTokens[asset] = adaLeft\n .mul(targetWeights[asset])\n .div(prices[asset])\n .add(amount)\n .reduce();\n }\n }\n\n const mtkPrice = tvl.div(new BigRational(state.mtkSupply, 1n));\n const newMtkSupply = tvl.add(adaInput).div(mtkPrice).reduce();\n return { assets: maybeBalancedTokens, mtkSupply: newMtkSupply };\n}\n\n/**\n * This function returns the amount of tokens that would end up in the portfolio\n * if the input is used to balance the portfolio.\n * @param prices The prices of the assets in ADA\n * @param targetWeights The target weights of the assets in the portfolio\n * @param adaPerToken The amount of ADA per token in the portfolio\n * @param tvl The total value locked in the portfolio\n * @param adaAvailable The amount of ADA available to balance the portfolio\n *\n * @returns The amount of tokens that would end up in the portfolio and how much\n * ADA would be left after the interaction\n *\n */\nfunction getTokensToBalance(\n prices: types.Prices,\n targetWeights: types.Weights,\n adaPerToken: types.RationalDict,\n tvl: BigRational,\n adaAvailable: BigRational,\n): [types.RationalDict, BigRational] {\n /** The actual token ratio of the portfolio */\n const weights: types.RationalDict = {};\n for (const [asset, adaEqAmount] of Object.entries(adaPerToken)) {\n weights[asset] = adaEqAmount.div(tvl).reduce();\n }\n\n // Already balanced => No changes needed\n if (\n Object.entries(targetWeights).every(([asset, targetWeight]) =>\n targetWeight.eq(weights[asset]),\n )\n ) {\n return [\n Object.fromEntries(\n Object.entries(targetWeights).map(([asset, weight]) => [\n asset,\n tvl.mul(weight).div(prices[asset]).reduce(),\n ]),\n ),\n adaAvailable,\n ];\n }\n\n /**\n * Base case for minimum tvl to balance can't be a token with target 0 as it may not be balanceable\n */\n const maybeBaseCase = Object.entries(adaPerToken).find(([asset]) => {\n const targetWeight = targetWeights[asset];\n assert(targetWeight, new Error('Invalid portfolio weights'));\n return !targetWeight.eq(ZERO);\n });\n\n assert(maybeBaseCase, new Error('Invalid portfolio assets'));\n const [baseCaseAsset, baseCaseValue] = maybeBaseCase;\n const baseCase = baseCaseValue.div(targetWeights[baseCaseAsset]);\n\n /**\n * The minimum balanced TVL if no tokens are removed in a deposit (or inserted in a withdraw) is determined by\n * the token for which, if nothing is added to it, the portfolio\n * needs the most (hence maxRational) ADA to complete the rest of\n * the ratios.\n *\n */\n const minTvlIfBalancedAndNoTokensRemovedOnDepositNorAddedOnWithdraw =\n Object.entries(adaPerToken).reduce((acc, [asset, assetValue]) => {\n // skip zero target weight\n if (targetWeights[asset].eq(ZERO)) {\n return acc;\n }\n /** Check if this is the token that needs the most (least in case of withdrawal) ADA to complete the rest */\n const tvlIfThisTokenAmountDoesntChange = assetValue.div(\n targetWeights[asset],\n );\n\n return adaAvailable.gte(ZERO)\n ? maxRational(tvlIfThisTokenAmountDoesntChange, acc)\n : minRational(tvlIfThisTokenAmountDoesntChange, acc);\n }, baseCase);\n\n /**\n * How much the input should be to have a a perfect balance after\n * the interaction (restricting to the tokens with non-zero weights\n */\n const tvlOfTokensWithZeroWeight = Object.entries(targetWeights)\n .filter(([_asset, weight]) => weight.eq(ZERO))\n .reduce((acc, [asset]) => {\n return acc.add(adaPerToken[asset]).reduce();\n }, ZERO);\n\n const tvlOfNonNullWeights = tvl\n .add(tvlOfTokensWithZeroWeight.negate())\n .reduce();\n\n const adaDiffToBalance = adaAvailable.gte(ZERO)\n ? minTvlIfBalancedAndNoTokensRemovedOnDepositNorAddedOnWithdraw\n .add(tvlOfNonNullWeights.negate())\n .reduce()\n : minTvlIfBalancedAndNoTokensRemovedOnDepositNorAddedOnWithdraw.add(\n tvl.negate(),\n );\n // If there is enough input to get to a balanced state\n const enoughAdaToBalance = adaAvailable.gte(ZERO)\n ? /*\n * If the input is positive, then the portfolio can be balanced with this\n * this interaction if the adaNecessaryToBalance is less than the input\n * Enough ADA (equivalent) coming in to add to the tokens that need it\n */\n adaDiffToBalance.lte(adaAvailable)\n : /*\n * If the input is negative, then the portfolio can be balanced with this\n * this interaction if the adaNecessaryToBalance is greater than the input\n * Removing enough ADA (equivalent) to the tokens that have too much\n */\n adaDiffToBalance.gte(adaAvailable);\n\n if (enoughAdaToBalance) {\n const balancedTokens: types.RationalDict = {};\n for (const [asset, targetWeight] of Object.entries(targetWeights)) {\n if (targetWeight.eq(ZERO) && adaAvailable.gte(ZERO)) {\n balancedTokens[asset] = adaPerToken[asset].div(prices[asset]).reduce();\n } else {\n balancedTokens[asset] =\n minTvlIfBalancedAndNoTokensRemovedOnDepositNorAddedOnWithdraw\n .mul(targetWeight)\n .div(prices[asset])\n .reduce();\n }\n }\n const adaLeft = adaAvailable.add(adaDiffToBalance.negate()).reduce();\n return [balancedTokens, adaLeft];\n }\n // there is not enough to balance it out\n else {\n const approximatedBalance: types.RationalDict = {};\n for (const [asset, assetAda] of Object.entries(adaPerToken)) {\n if (targetWeights[asset].eq(ZERO) && adaAvailable.gte(ZERO)) {\n approximatedBalance[asset] = assetAda.div(prices[asset]).reduce();\n } else {\n /**\n * How much of a given token is missing (or too much of) to reach\n * perfect balance\n */\n const tokenAdaDiffToBalance =\n minTvlIfBalancedAndNoTokensRemovedOnDepositNorAddedOnWithdraw\n .mul(targetWeights[asset])\n .add(assetAda.negate());\n\n approximatedBalance[asset] = adaAvailable\n .mul(tokenAdaDiffToBalance)\n .div(adaDiffToBalance)\n .div(prices[asset])\n .add(assetAda.div(prices[asset]))\n .reduce();\n }\n }\n const adaLeft = ZERO;\n return [approximatedBalance, adaLeft];\n }\n}\n\n/**\n * Computes how much of each fee in the smart contract this interaction contains\n */\nexport function computeFees({\n portfolioState,\n amount,\n type,\n}: types.FeeComputation) {\n const batcherFee = portfolioState.batcherFee;\n\n const platformFee = amount\n .multipliedBy(portfolioState.platformFee)\n .div(10_000);\n\n const microMTKsInOrder = amount.div(portfolioState.microMtkPrice);\n\n // divided by 10_000 to turn the fee into a multiplying factor\n const userFee =\n type === 'mint'\n ? microMTKsInOrder.multipliedBy(portfolioState.entryFee).div(10_000)\n : microMTKsInOrder.multipliedBy(portfolioState.exitFee).div(10_000);\n\n return {\n /**\n * Batcher fee in lovelace\n */\n batcherFee: batcherFee.abs(),\n /**\n * Platform fee in lovelace\n */\n platformFee: platformFee.abs(),\n /**\n * User fees in microMTKs\n */\n userFee: userFee.abs(),\n };\n}\n","export const MTK_DECIMALS = 6;\n\nexport const FEES = {\n entry: {\n max: 500n,\n min: 1n,\n },\n exit: {\n max: 500n,\n min: 1n,\n },\n batcher: {\n max: 4_000_000n,\n min: 1n,\n },\n platform: {\n max: 100n,\n min: 1n,\n },\n} as const;\n"]}